Coming of age … Andile Gumbi as Simba in The Lion King, which has been running in London’s West End since October 1999. Photograph: Simon Turtle /Disney

Cats may have slunk away into the night, but The Lion King, it seems, roars on forever. The musical of the Disney cartoon, which has been running in London's West End since October 1999, said today it had broken its own box office record, taking more than £34m during 2010 - £2m more than the previous year - and ending the year with its best ever week of ticket sales.

Big musicals are so far defying the economic gloom, and theatre in general is proving surprisingly resilient.

Another musical, Wicked, a prequel to the Wizard of Oz, has also just hit the record books, taking £1,002,885 at the box office in a week, the highest takings for a single week in London theatre history, although it was behind The Lion King across the year, taking £30m.

Scott Matthewman, of the Stage, said: "It looks as if a big family outing to a big West End show is not necessarily counted as discretionary spending, in the way that regular cinemagoers might cut back. The shows which generate repeat visits, and target a family audience – like The Lion King – are doing particularly well. The Lion King, with the might of Disney behind it, is also putting a lot into education outreach work, so if school children are going to pester to be taken to one London show, that's going to be the one."

The Lion King, a coming-of-age story about the cub Simba, has become far more successful than the film that inspired it. More than 820,000 people saw the London show in 2010, and more than nine million have watched it in the city since it began its run.

Productions are running in Germany, Tokyo, and in America in a touring version, in Las Vegas, and on Broadway, where it opened in 1997. Yesterday, with its 5,462nd performance, it became the seventh longest running show in Broadway history. It has now been seen by an estimated 54 million people in 15 countries and translated into five languages.

Worldwide, it has generated £2.7bn at the box office, and probably as much again in undisclosed revenue from soundtrack recordings, video games, T-shirts, and other merchandise.

"I don't see it coming to an end," said David Schrader, executive vice-president and managing director of Disney's theatre productions.

The Lion King has proved a fairy godmother to the Theatres Trust, which campaigns to preserve all theatres in the UK, and which owns the freehold of its home, the Lyceum theatre in central London.

Mhora Samuel, director of the trust, said: "We don't get a commercial rent, that goes to the leaseholders, but we do get a small return from ticket sales, which has been wonderful for us."

She has seen it three times: "It's one of the few big shows in the West End that suits every member of a family, even very small children. The success of The Lion King shows that the West End could probably do with more shows for that audience."

In New York, where the show didn't cancel a single performance when record snow falls hit the city and audiences hiked to see it, Schrader said: "It really doesn't seem possible that it is more than 10 years. I have a lot more grey hairs, but the show still has a freshness and an authenticity that is winning over new audiences.

"We're now at the stage where people who started their careers in our show are spreading out and populating many other productions, which is pretty exciting for us."

A team of more than 100 people is behind all the different productions, including talent scouts for the young South African performers who have appeared in every production. It has won numerous awards for its sets and costumes, and mixing actors and puppets has given the show a completely different look from the film.

The show's director, Julie Taymor, an unusual choice at the time for a commercial musical, studied Oriental and Javanese puppetry, and after graduating founded her own theatre company in Bali.

She was also head of design, and in London the attention to detail extended to painting the entire Lyceum theatre, which was formerly derelict, in shades of ochre to complement the sets.

The Lion King on Broadway won Taymor two Tony awards, for design and direction, making her the first woman to win the award for directing a musical.

She is currently wrestling with a far more problematic Broadway musical based on a cartoon, Spider-Man, with special effects including spectacular aerial acrobatics, and a score by U2's Bono and the Edge.

The show reached the stage almost a year late, because of extra fundraising to cover rocketing costs – it has a $65m (£42m) budget – and after weeks of previews is still dogged by technical problems.

An actor suffered several broken bones in one accident, while the actor playing the villain walked out after a concussion to her head.

The Lion King still has some way to go to become the West End's most successful musical. Andrew Lloyd Webber's Cats held the record when it closed in 2002 after 8,949 performances over 21 years, but has since been overtaken by Les Misérables, Willy Russell's Blood Brothers and Lloyd Webber's The Phantom of the Opera.

But The Lion King has outlived a string of other musicals which also seemed set to occupy the West End forever, including Starlight Express, which closed in 2002, Spamalot, which closed in 2009, and Hairspray, which closed last year.